Denote the eigenvalues of \(A\)  by \(0 < \lambda _1 \le \cdots \le \lambda _n\) .
The standard Rayleigh–Ritz extraction enjoys a good reputation for exterior eigenvalues (see, e.g., [1]}), which means the largest or smallest few eigenvalues, in our case of symmetric \(A\) . However, for interior eigenvalues near a target \(\tau \in (\lambda _1, \lambda _n)\) , the harmonic Rayleigh–Ritz extraction tends to produce approximate eigenvectors of better quality. This approach works as follows (see, e.g., [2]} for more details).
